Final Exam STATS 1430 (carmen homeworks)
If you reject Ho, which type of error could you be making? -Could make both Type 1 and Type 2 errors -Type 2 error -Type 1 error -No error is made, your conclusion is correct.
Type 1 error
True or false? The significance level is the same as a Type 2 error.
false
True or false? The value of α will change if you get a new data set.
false
What is the name for the cutoff value that lets you decide between rejecting Ho and failing to reject Ho with your p-value? Z-level confidence level significance level
significance level
If X is a binomial random variable with n = 4 and p = 0.18. What is P(X = 3)? 0.981 0.019 0.75 0.18
0.019
Suppose X = exam score and X has a normal distribution with mean 80 and standard deviation 5. Bob scored at the 90th percentile. What is Bob's Z-value (aka Z-score)? 1.28 10% 86.4 2
1.28
If an observation has a z-score of -1.5, how many standard deviations is it above or below the mean? 1.5 standard deviations below the mean 1.5 standard deviations above the mean 0.066 standard deviations above the mean 0.066 standard deviations below the mean
1.5 standard deviations below the mean
If your confidence interval is 95%, what is the value of Z that goes into the confidence interval formula? 1.96 1.645 2.58 None of the other choices is correct
1.96
Suppose X has a uniform distribution on the interval [0,10]. What is f(x)? 1/10 10 Not enough information to tell
1/10
Let f(x) = kx where x is between 0 and 2. What is the value of k that makes this a legitimate density function? 1/2 None of the other choices is correct 4 2
1/2
f(x) = 1/2 between 0 and 2. What is the probability that X is between 1 and 3? 0 1/2 1
1/2
Suppose 40% of college students plan to vote in the election. Now suppose we randomly select 200 college students and ask them if they plan to vote. What is the probability that more than 75 of the 200 students sampled plan to vote? 37.5% 40% 76.4% 24.6%
76.4%
Suppose X has a normal distribution with mean 80 and standard deviation 5. What is the 90th percentile of X? 90 86.4 .90 73.6
86.4
True or false? When you integrate e^(-x), you get e^(-x)
False
True or false? If your test statistic is negative, so is your p-value.
False
True or false? The margin of error increases if the sample size increases.
False
Which of the following describes the relationship between parameters and statistics? -We use parameters to estimate or test statistics -Statistics and parameters are the same thing -We use statistics to estimate or test parameters
We use statistics to estimate or test parameters
If X does not have a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar? X-bar is exactly normal for any n X-bar is exactly normal if n > 30 X-bar is approximately normal if n > 30 X-bar is approximately normal for any n
X-bar is approximately normal if n > 30
If X is a binomial random variable with n = 15 and p = 0.3, can we use the normal approximation?
no
When you take the given information and form a Z-score in a hypothesis test for the mean, what is the special name of that result? test statistic descriptive statistic sample statistic
test statistic
A continuous random variable has a(n) __________________________ number of possible values. -finite -uncountably infinite -countably infinite
uncountably infinite
If the variance of X is 10, what is the variance of 4X + 20? 160 60 180 40
160
The mean temperature in Cancun is 28.5 degrees Centigrade (Celsius). What is the mean temperature in Cancun in Fahrenheit? Note: F = 9/5C + 32 -28.5 -83.3 -51.3 -None of these choices is correct.
83.3
Bottles of cream have a normal distribution with mean 8 ounces. You would stop the process if the containers were being filled incorrectly. What is your alternative hypothesis? Ha: u < 8 None of the other answers is correct. Ha: u not equal to 8 Ha: u > 8
Ha: u not equal to 8
Everyone at Bob's diner makes $12.00 per hour. Let X = salary of an employee at Bob's diner. What is the mean of X? Not enough information to tell. $12 per hour $0 dollars per hour
$12 per hour
Where is the 10th percentile of the Z distribution? 0.90 - 1.28 1.28 0.10
-1.28
Bottles of cream have a normal distribution with mean 8 ounces. You would stop the process if the containers were being filled incorrectly. Your sample of 30 containers has an average weight of 7.7 ounces. Assume the standard deviation is .8. What is your test statistic? -0.375 7.7 2.05 -2.05
-2.05
The mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is .35. If the price increases by 25 cents a box, what is the new variance? .35 .60 None of the other choices is correct $4.25
.35
Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x)^2, 0 < x < 3 What is P(X=2)? 0 4/9 Can't tell from info given
0
What is the probability that a normally distributed random variable X is greater than 85 if μX= 75 and σX= 4? CHOOSE THE CLOSEST ANSWER. 2.5 1 0.006 0.994
0.006
Let f(x) = 3(x)^2 for 0 < x < 1 What is the median of X? Choose the closest answer! 0.8 0.6 0.4 0.2
0.8
If your p-value is .11, and the significance level is .05, what do you conclude? Fail to reject Ho Not enough information to tell Reject Ho
Fail to reject Ho
Suppose f(x) = 1/2 where 0 < X < 2. True or false? The median of X is 0.50.
False
(T/F) A probability density function f(x) tells you how much probability is in the area near x.
True
Everyone at Bob's diner makes $12.00 per hour. Let X = salary of an employee at Bob's diner. With this information, can you find the variance of X? True False
True
True or False? The 80th percentile of the standard normal (Z) distribution is .84
True
How large does n generally have to be in order for the Central Limit Theorem to take effect? (Assume X does not have a normal distribution.) np at least 10 and n(1-p) at least 10 n can be any value np ≥ 10 n > 30
n > 30
Let X = time waiting in line at a restaurant to get a seat in minutes. What are the units of the variance of X? Choose the best answer. -no meaningful units -square minutes -minutes -None of the other choices is correct
no meaningful units
Bob's alternative hypothesis is Ha: u > 8 and his test statistic is 1.75. What is Bob's p-value? 0.0401 0.9599 0.4599 0.0802
0.0401
Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x)^2, 0 < x < 3 True or false? The median of X is 1.5.
False
Suppose X is a discrete random variable with mean 10 and variance 4, and Y is a discrete random variable with mean 20 and variance 9. We do not know whether X and Y are independent. True/False: We can find the variance of X+Y with only the information we are given.
False
True or False? If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.7738
False
True or false? Let X be a continuous random variable. Then f(x) must always lie between 0 and 1.
False
True or false? Failing to reject Ho and Accepting Ho are both appropriate conclusions that mean the same thing.
False
A company has developed a new battery, but the average lifetime of all of the batteries it makes is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a: statistic population parameter sample
statistic
True or False? With a continuous random variable, P(a < X < b) is the area under the curve f(x) between a and b.
True
True or False? μ(x-y)= μ(x)-μ(y)
True
True or False? A confidence interval for the mean is known as a range of likely values for the population mean.
True
True or False? Suppose X and Y are independent. Then is the following TRUE or FALSE? σ^2 (x-y)= σ^2 (x) + σ^2 (y)
True
True or False? The margin of error is larger if the standard deviation of the population increases (assume all else stays the same.)
True
True or False? The margin of error of a confidence interval gets larger if the confidence level increases (assume all else stays the same.)
True
If X has a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar? -X-bar is exactly normal if n > 30 -X-bar is approximately normal if n > 30 -X-bar is approximately normal for any n -X-bar is exactly normal for any n
X-bar is exactly normal for any n
When you use the normal distribution to find a probability for a binomial random variable, which of the following is true? -You needed np and np(-p) to be less than 10. -You are making a mistake. -None of the other choices is correct -You needed np and n(1-p) to be at least 10 and you get an approximate answer.
You needed np and n(1-p) to be at least 10 and you get an approximate answer.
Which of the following is NOT a condition of the binomial distribution? -fixed number of trials (n) -two possible outcomes on each trial (yes/no) -same probability of yes on each trial (p) -independent trials -all of these choices are conditions of the binomial
all of these choices are conditions of the binomial
A discrete random variable can be finite or uncountably infinite. (T/F)
False
Let f(x) = 3(x)^2 for 0 < x < 1 True or false? P(X<1/2) = P(X<=1/2)
True
Bob wants a 95% confidence interval for the population mean. Previous research shows the population standard deviation is 8. He wants his margin of error to be no more than 4. What should his sample size be? 4 15 16
16
Suppose X and Y are independent. Then is the following true or false? σ(x+y)= σ(x) + σ(y)
False
Suppose Bob makes a 95% confidence interval and his result is (70, 90). True or false: We can tell what Bob's sample mean must have been.
True
Let X = time waiting in line at a restaurant to get a seat. Mean of X = 20 min, Variance of X = 25 Let Y = time waiting for your food to arrive. Mean of X = 30 min, Variance of Y = 36 X and Y are correlated and the correlation is 0.80. What is the variance of the TOTAL TIME waiting? None of the other choices is correct 61 109 121
109
(T/F) The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. The percentage of the students which take longer than 80 minutes to complete the exam is 84.13%.
False
Which of the following is NOT a continuous random variable? -Length of time between accidents at an intersection -Time waiting on the phone for tech support (in seconds) -Number of accidents in one year at an intersection -All of the choices are continuous random variables
Number of accidents in one year at an intersection
Which of the following is true about the standard error of the random variable X-bar as n increases? -Not enough information to tell. -The standard error of X-bar increases. -The standard error of X-bar decreases. -The standard error of X-bar stays the same.
The standard error of X-bar decreases.
Which of the following terms represents "all possible values of a random variable and how often you expect them to occur?" -probability distribution -data distribution -none of these choices is correct -population
probability distribution
Your friend claims the average price of a burger in the Columbus Gateway Area is $10.00. You believe it's lower than that. What symbol represents the $10 in this scenario? x-bar μX μ0
μ0
True or False? We are 100% confident that our SAMPLE mean is in every confidence interval we make.
True
Suppose X has a normal distribution with mean 80 and standard deviation 5. How many standard deviations above or below the mean is 70? 2 standard deviations below the mean 2 standard deviations above the mean 10 standard deviations below the mean None of the other choices is correct
2 standard deviations below the mean
Suppose X has a normal distribution and you run a hypothesis test with Ho: u = 8 and Ha: u > 8. You collect a random sample of n = 11 values, and you find your test statistic is t = 2.50. What two values does the p-value lie between on the t-table? .01 < p value < .025 .005 < p value < .01 .025< p value < .05 None of the other choices is correct
---
t(n-1) is a value on the t distribution with ______________________________ n-1. -degrees of freedom -mean -standard deviation
degrees of freedom
True or false? A Type 2 error is described as a false alarm.
false
True or false? The t distribution is taller and thinner (more concentrated around the mean) than the Z distribution.
false
If you don't know the population standard deviation, what do you use as a substitute in your test statistic? uo (stands for mu sub zero) sigma x-bar s
s
True or false? The larger n is, the closer the t distribution looks to the Z distribution.
true
Suppose a 95% confidence interval for the mean is (10, 12) when you know the value of the population standard deviation (sigma). If you HAD NOT known the value of sigma, would your confidence interval have been wider, narrower, or the same? the same wider narrower
wider
Suppose you want to estimate the average age of all Pokemon players. Would you use a confidence interval or a hypothesis test?
confidence interval
True or false? A confidence interval is narrower if you use t than if you use Z. (Assume all else is the same.)
False
X p(x) 1 1/2 2 1/4 3 1/4 True/False: The mean of X is 2
False
Suppose X has a normal distribution and you run a hypothesis test with Ho: u = 8 and Ha: u > 8. You collect a random sample of n = 11 values, and you find your test statistic is t = 2.50. What is your decision?
Reject Ho
The set of all possible sample means from all possible samples of size n from the population is known as the: -Sampling distribution of X-bar -Not enough information to tell -Sample mean of the population of X -Population probability distribution of X
Sampling distribution of X-bar
True or False? The p-value will change if you get a new data set.
True
Suppose 20% of Ohio residents support the legalization of marijuana. If you randomly select n people and would like to use the normal approximation to answer questions, what does your sample size have to be, at minimum? 20 80 50 10
50
Suppose someone claims the average delivery time for U.S. packages to be delivered during December is 2 days. You believe it takes longer than that. You conduct a hypothesis test; what are your hypotheses? Ho: X-bar = 2 vs. Ha: X-bar ≠ 2 Ho: µ >2 vs. Ha: µ ≤ 2 Ho: X-bar = 2 vs. Ha: X-bar > 2 Ho: µ = 2 vs. Ha: µ >2
Ho: µ = 2 vs. Ha: µ >2
Which of the following is true about the mean of the random variable X-bar as n increases? -Not enough information to tell -The mean of X-bar increases -The mean of X-bar stays the same -The mean of X-bar decreases
The mean of X-bar stays the same
Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x)^2, 0 < x < 3 What is the probability that x is greater than 2? 0 None of these choices is correct. .3 .7
0.7
Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x)^2, 0 < x < 3 What is the mean of X? 2.25 3 1.5 0.11
2.25
Which of the following is NOT a discrete random variable? -One that is finite. -All of these answers are discrete random variables. -One that is countably infinite. -One that is uncountably infinite.
One that is uncountably infinite.
Suppose X = number of 1 foot long steps taken in one hour by a person working in a bank. Suppose the mean of X is 300 and the variance is 64. If you change the units from feet to inches, you multiply by 12. What is the new standard deviation? Square root of (12 x 64) Square root of (12^2 x 64) 12^2 x 64 12 * 64
Square root of (12^2 x 64)
The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given? 74.8 minutes 92.3 minutes 84.7 minutes 78.4 minutes
78.4 minutes
The Central Limit theorem tells us important results that pertain to: -The standard error of the distribution of X-bar -The mean of the distribution of X-bar -All of the above -The shape (type) of the distribution of X-bar
The shape (type) of the distribution of X-bar
Which of the statements below is correct? -The standard deviation of X is the square root of the variance of X. -None of the other choices is correct -The standard deviation of X is the same as the variance of X. -The standard deviation of X is the square of the variance of X.
The standard deviation of X is the square root of the variance of X.
The mean cost of a box of Cheerios Oat Crunch is $4.00. If the price increases by 10% what is the new mean? $4.00 $4.40 None of the other choices is correct $4.10
$4.40
The national proportion of adults who are concerned about nutrition is 0.4. You take a random sample of 10 adults and count the number who are concerned about nutrition (call it X). What is the probability that X is less than 2? 0.9537 0.6 0.0463 None of the choices are correct
0.0463
In testing the hypotheses 800 vs Ho: µ≠800, if the value of the test statistic equals 1.75, then the p-value is: 0.0802 0.9599 None of the other choices is correct 0.0401
0.0802
X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that X will be less than 55? 0.023 0.841 0.159 0.977
0.841
X p(x) 1 0.1 2 0.3 3 0.6 What is the probability that X is at least 2? 0.90 0.10 0.30 0.40
0.90
Let f(x) = 3(x)^2 for 0 < x < 1 What is P(X < 1/2)? Choose the closest answer! 1/8 1 1/4 1/2
1/8
Mean of (X-Y) = Mean of X - Mean of Y (T/F)
True
Let f(x) = 3(x)^2 for 0 < x < 1 What is the mean of X? Choose the closest answer! 1 1/4 3/4 2/4
3/4
Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x)^2, 0 < x < 3 What is f(2)? 4/9 0 Can't tell with info given
4/9
Bob makes a 95% confidence interval with a random sample of 100 and his margin of error is plus or minus 18. In order to cut the margin of error in half next time, what should Bob's sample size be? (Hint: You CAN determine the answer without knowing the standard deviation.) 50 400 10,000 200
400
What is the symbol we use to represent the mean of the random variable X-bar? -Capital X-bar -Mu with subscript X-bar -Mu with subscript X
Mu with subscript X-bar
If X and Y are independent, then True/False: Variance of (X-Y) = Variance of (Y-X)
True
Suppose X = number of women in a sample of size 100 from a population that has 80% women and 20% men. X has an approximate normal distribution with mean _____ and standard deviation ______. 80,4 80,16 50,5
80,4
Suppose X has a uniform distribution on the interval [0,10]. True or false, the mean of X is 5.
True
True or false? Suppose n = 10 and you want the value of t to put in your 95% confidence interval for the mean, where you don't know the population standard deviation. The value of t that you find on the t-table in this case is 2.2622.
True
True or false? You must use a t instead of a Z in your confidence interval formula for a mean when you don't know the value of sigma. (Assume you have a normal distribution.)
True
True or false? If you reject Ho in a hypothesis test for the mean, the value of uo is guaranteed not to be in the corresponding confidence interval. (Assume Ha is , alpha = .05, confidence level = 95%)
True
Suppose someone reports that the average age of all Pokemon players is 13. You believe it's higher than that because your statistics professor plays Pokemon. You decide to challenge the claim. Do you use a confidence interval or a hypothesis test? -confidence interval -hypothesis test -either a hypothesis test or a confidence interval
hypothesis test
True or false? If Ha is not equals, you have to double the probability of being beyond your test statistic to get your p-value.
True
Which of the following variables has a binomial distribution? -Flipping a coin until you get 10 heads and counting the number of flips needed. -Flipping a coin 10 times and counting the number of heads. -Both of these choices have binomial distributions. -Neither of these choices has a binomial distribution.
Flipping a coin 10 times and counting the number of heads.
Suppose a pizza place claims it's average pizza delivery time is 10 minutes. Bob makes a 95% confidence interval for the average pizza delivery time for this pizza place and gets (15, 20). What does Bob think about the pizza place's claim? He disagrees with the claim. He can't disagree with the claim.
He disagrees with the claim.